Please use the correct time complexity

Problem #2: (45 pts) (a) Consider a binary min-heap. Assume that we have a method that print the keys as encountered in a preorder traversal. Is the output sorted? Justify your answer. Attempt the same question for inorder and postorder traversal (b) Propose a O(n) running time complexity algorithm (only pseudo-code) to find all nodes less than some value X in a binary min-heap. Analyze its complexity. Justify (c) Show the result of inserting 10, 12, 1, 14, 6, 5, 8, 15, 3, 9, 7, 4, 11, 13, and 2, one at a time and in the giver order, into an initially empty binary min heap (d) Show the result of performing three deleteMin operations in the heap of the previous binary min heap (e) Write a method replaceKey in the MinHeap class with the following signature public void replaceKey (Integer oldKey, Integer newKey) The method will replace the first occurrence of oldKey with the newKey, and restore the Min-Heap property after the change. If the oldKey does not exist in the heap, the method prints an appropriate message and returns without changing the heap Example: Suppose our binary heap object (bh) has the following keys 32 19 kxo 4 64 26 99 42 54 28 Then the method call: bh.replaceKey (oldKey Integer (54), newKey Integer(2)) should change the keys to: x2 4 32 6 64 26 99 42 19 28 Note: You can assume that the methods perlocateUp and perlocateDown are already implemented in your MinHeap class